Skip to main content
SpringerLink
Log in

Caterpillars and context-free languages

  • Conference paper
  • First Online:
STACS 90 (STACS 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 415))

Included in the following conference series:

Abstract

We use the concept of a caterpillar tree to study the properties of context-free languages, in particular new results about the index of context-free languages and the recognition of context-free languages are obtained this way. The first group of results points to differences between ambiguous and unambiguous languages. For unambiguous languages we prove the existence of a gap between finite index and O(log n) index. For ambiguous languages there is no such a gap: we prove the existence of grammars with infinite but arbitrarily slowly growing index. We show that bounded languages are of finite index and give a deterministic log space algorithm for the recognition of deterministic finite index languages. We also describe a parallel algorithm recognizing deterministic context-free languages on a CREW-PRAM with O(n 2) processors in time O(log2 n).

The work of this author was partly done during his stay at the University of Paderborn and was supported by the German Research Association (DFG)

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Alt, H., Lower bounds on space complexity of context-free recognition, AI 12 (1979), 33–61

    Google Scholar 

  2. Brainerd, B., An analog of a theorem about context-free languages, Information and Control 11 (1968), 561–567

    Article  Google Scholar 

  3. von Braunmuehl, B., Cook, S., Mehlhorn, K., Verbeek, R., The recognition of deterministic CFLs in small time and space, Information and Control 56 (1983), 34–51

    Article  Google Scholar 

  4. Chytil, M., Crochemore, M., Monien, B., Rytter, W., On the parallel recognition of unambiguous context-free languages, submitted for publication

    Google Scholar 

  5. Chytil, M., Jakl, V., Serial composition of 2-way finite state transducers and simple programs on strings, Proc. of ICALP'77, LNCS 52, Springer-Verlag 1977, 135–147

    Google Scholar 

  6. Chytil, M., Monien, B., Caterpillars and Context-free languages, technical report no. 56, University of Paderborn, October 1988

    Google Scholar 

  7. Dymond, P.W., Ruzzo, W.L., Parallel RAMs with owned global memory and deterministic context-free language recognition, Proc. ICALP'86, Lecture Notes in Computer Science 226 (1986), 95–104

    Google Scholar 

  8. Ehrenfeucht, A., Rozenberg, G., Vermeir, D., On ETOL systems with finite tree rank, SIAM J. Comput. 10 (1981), 40–58

    Article  Google Scholar 

  9. Gibbons, A., Rytter, W., Efficient Parallel Algorithms, Cambridge University Press, 1988

    Google Scholar 

  10. Ginsburg, S., Spanier, E., Derivation — bounded languages, JCSS 2 (1968), 228–250

    Google Scholar 

  11. Gruska, J., A few remarks on the index of context-free grammars and languages, Information and Control 19 (1971), 216–223

    Article  Google Scholar 

  12. Hopcroft, J.E., Ullman, J.D., Formal languages and their relation to automata, Addison-Wesley, Reading, Mass. 1969

    Google Scholar 

  13. Jones, N.D., Skyum, S., Recognition of deterministic ETOL languages in logarithmic space, Information and Control 35 (1977), 177–181

    Article  Google Scholar 

  14. Klein, P.N., Reif, J., Parallel time O(log n) acceptance of deterministic CFLs on an exclusive-write P-RAM, SIAM J. Computing 17 (1988, 463–485

    Article  Google Scholar 

  15. Latteaux, M., Thierrin, G., On bounded cf-languages, EIK 20 (1984)

    Google Scholar 

  16. Meggido, N., Hakimi S.L., Garey, M.R., Johnson, D.S., Papadimitriou, C.H., The complexity of searching a graph, Proc. FOCS'81, 376–385

    Google Scholar 

  17. Ruzzo, W.L., Tree-size bounded alternation, JCSS 21 (1980), 218–235

    Google Scholar 

  18. Rytter, W., Parallel time O(log n) recognition of unambiguous CFL's, Proc. FCT'85, Lecture Notes in Computer Science 199 (1985), 380–389

    Google Scholar 

  19. Salomaa, A., On the index of a context-free grammar and language, Information and Control 14 (1969), 474–477

    Article  Google Scholar 

  20. Salomaa, A., Formal language theory, Academic Press 1973

    Google Scholar 

  21. Wechsung, G., The oscillation complexity and a hierarchy of context-free languages, Proceedings of FCT'79, L. Budach (ed.), Akad. Verlag Berlin 1979, 508–515

    Google Scholar 

  22. [Ynt]Yntema, M., Inclusion relations among families of context-free languages, Information and Control 10 (1967), 572–597.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Charles University, Malostranske nam. 25, CS-11800, Praha 1

    Michal P. Chytil

  2. Math. and Computer Science, University of Paderborn, D-4790, Paderborn

    Burkhard Monien

Authors
  1. Michal P. Chytil
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Burkhard Monien
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Christian Choffrut Thomas Lengauer

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chytil, M.P., Monien, B. (1990). Caterpillars and context-free languages. In: Choffrut, C., Lengauer, T. (eds) STACS 90. STACS 1990. Lecture Notes in Computer Science, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52282-4_33

Download citation

  • DOI: https://doi.org/10.1007/3-540-52282-4_33

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52282-9

  • Online ISBN: 978-3-540-46945-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation